Knowing the properties and locations of underground rock formations is useful for making decisions as to where and how to economically produce hydrocarbons from underground reservoirs. In the field of hydrocarbon exploration and production, seismic imaging techniques may be used to gain an understanding of the depth and structures of subsurface geological formations. Various seismic sources, such as dynamite, “thumper” trucks, air guns, and other noise sources located at the surface of a hydrocarbon bearing field, may be used to propagate seismic waves through an underground formation. The propagated waves are reflected through the formation and acquired using various seismic signal receiver devices, for example, geophones, hydrophones, and the like. Seismic-data traces including a record of the sound wave reflections acquired from the underground formation may be used to generate three-dimensional images of subsurface geological structures, including faults and other stratigraphic features that trap hydrocarbon and mineral deposits.
Seismic imaging becomes more complex when the subsurface formation has fractures, a preferred orientation of grains, tectonic stress regimes or other geo-mechanical variations. In such cases, the subsurface medium of the formation layer being imaged may exhibit seismically anisotropic characteristics. Such anisotropy may be effectively modeled with orthorhombic media parameters, which provide greater degrees of freedom relative to other higher symmetries of anisotropy. Orthorhombic media parameters may be used to produce more accurate images of subsurface structures at varying depths within the formation. However, the increased number of parameters per layer adds to the complexity of the inverse problem that is generally used to extract such parameters from observed seismic data. Additionally, such parameter extraction becomes even further complicated in cases where the subsurface is composed of non-horizontal or non-flat layers.